Weighted approximation of functions with singularity by Stancu operators

2013 ◽  
Vol 2013 (1) ◽  
pp. 31
Author(s):  
Shanshan Gao ◽  
Keyword(s):  
Weighted Approximation ◽  
Approximation Of Functions ◽  
Stancu Operators

Weighted Approximation of Functions with Inner Singularities by Exponential Weights in [−1, 1]

2003 ◽  
Vol 24 (1-2) ◽  
pp. 181-194
Author(s):  
Biancamaria Della Vecchia ◽  
Giuseppe Mastroianni ◽  
Jozsef Szabados
Keyword(s):  
Weighted Approximation ◽  
Approximation Of Functions ◽  
Exponential Weights

scholarly journals Approximation properties of Jain-Stancu operators

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 1081-1088 ◽  
Author(s):  
Mehmet Özarslan
Keyword(s):  
Asymptotic Expansion ◽  
Error Estimation ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Linear Functions ◽  
Approximation Properties ◽  
Stancu Operators ◽  
Lagrange Expansion ◽  
Preserve Linear

In the present paper, we introduce the Stancu type Jain operators, which generalize the wellknown Sz?sz-Mirakyan operators via Lagrange expansion. We investigate their weighted approximation properties and compute the error of approximation by using the modulus of continuity. We also give an asymptotic expansion of Voronovskaya type. Finally, we introduce a modified form of our operators, which preserves linear functions, provides a better error estimation than the Jain operators and allows us to give global results in a certain subclass of C[0,?). Note that the usual Jain operators do not preserve linear functions and the global results in a certain subspace of C[0,?) can not be given for them.

scholarly journals Weighted approximation of functions on the real line by Bernstein polynomials

2004 ◽  
Vol 127 (2) ◽  
pp. 223-239 ◽  
Author(s):  
B. Della Vecchia ◽  
G. Mastroianni ◽  
J. Szabados
Keyword(s):  
Real Line ◽  
Bernstein Polynomials ◽  
Weighted Approximation ◽  
Approximation Of Functions ◽  
The Real
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